Method and system for characterization of knee joint morphology

ABSTRACT

A method and system for characterizing a knee joint in terms of its skeletal morphology. A plurality of loci associated with a model of skeletal structure of a knee joint are fitted and used to parameterize positions of the plurality of loci in a given subject and, thereby, to derive parameters of a deformable statistical template. The skeletal morphology is then characterized on the basis of the derived parameters of the deformable statistical template.

The present application claims priority from U.S. Provisional PatentApplication Ser. No. 60/664,912, filed Mar. 24, 2005, which isincorporated herein by reference.

TECHNICAL FIELD

The invention relates generally to the characterization of themorphology of knee joints, each knee joint at one or more times, forpurposes of research or for diagnosis of pathologies in a particularindividual.

BACKGROUND ART

Studies of the anatomy of the knee require quantitative characterizationof structural parameters. As one particular example, anatomical studiesof knees in identified populations require a measure of kneeosteoarthritis (OA), a slow progressive disease characterized by loss ofcartilage in the joint and leads to loss of joint movement and increasedpain. Of the two primary compartments (lateral and medial) of the knee,OA is seen mainly in the medial compartment, due to the higherweight-bearing load borne here. Longitudinal evaluation of the diseasein an individual relies on clinical and radiographic features, chieflypain, disability and structural changes. Disease-modifying therapies arecurrently under development and these will rely upon the accurate andprecise assessment of the progression of the disease.

In current practice, the primary endpoint used in population studies,clinical trials, and epidemiological studies of OA of the knee, is thesurrogate measure of radiographic minimum Joint Space Width (mJSW),measured between either of the weight-bearing surfaces of the femoralcondyles and the tibial plateau from a radiograph taken in a semi-flexedposition, as shown in the radiograph of FIG. 1. The progressive loss ofcartilage is measured by narrowing of the mJSW. Since OA is seen mainlyin the medial compartment, the mJSW is usually measured in thiscompartment only.

The measurement of mJSW is usually made by a trained physician using agraduated hand-held lens while reviewing the radiograph on a light-box.Using this method, it is difficult to avoid significant inter- andintra-observer variation due to the subjectivity of the human observer.Moreover, since the mJSW is usually only measured in the medialcompartment, it is possible that OA in the lateral compartment willelude detection, and indeed, some patients have primary lateralcompartment disease. Finally, in that the mJSW is a single measure ofdisease progression, effects in the whole joint may be masked byreliance on a single indicator.

In order to address the major problem of human subjectivity, computeranalysis of digitized knee radiographs for the measurement of mJSW hasbeen employed by several authors. One method of computer analysis forderiving mJSW from X-ray images was described by Duryea et al., 27 Med.Phys., pp. 580-91 (March, 2000), herein incorporated by reference.Moreover, surrogate outcome measures for characterizing the knee jointspace other than the mJSW, have been studied and compared with mJSW, forexample, by Duryea et al., 11 Osteoarthritis & Cartilage, pp. 102-110(2003), which is incorporated herein by reference. The foregoing methodsare examples of feature-based analytical techniques.

It is desirable, however, to supplement radiographic mJSW measurementwith a technique that contributes to greater sensitivity to OA inquantitative measures than is available using non model-basedapproaches, particularly with a view to clinical evaluation of potentialtherapies that may be performed more quickly with fewer patients byvirtue of the enhanced sensitivity.

SUMMARY OF THE INVENTION

In accordance with preferred embodiments of the present invention, amethod is provided for characterizing a knee joint in terms of a modelparameterization. The method has steps of:

a. creating a deformable statistical template characterized by a set ofparameters that, as a set, span an abstract vector space representingthe set of spatial positions of specified features of the knee joint,each vector uniquely describing its variation from a population mean;

b. fitting, at runtime, in a two-dimensional image of the skeleture of aknee, a plurality of loci associated with the specified features toallow parameterization in terms of a deformable statistical template;

c. parameterizing positions of the plurality of loci in a given subjectto derive values for parameters of the deformable statistical template;and

d. characterizing the skeletal morphology of the knee of the givensubject on the basis of either a subset of the plurality of loci, and/orthe derived parameters of the deformable statistical template.

It is to be understood that where the term “subset” is used in thedescription of the present invention or in any appended claim, inconnection with elements comprising a set, the term “subset” is to beunderstood as encompassing either a proper, or a full, subset of theentirety of the set of elements. Furthermore, the term “locus” is usedto mean one of the plurality of points within some “distance” of a point(in the vector space) that define a feature. “Distance” refers,generally, to a norm defined over the vector space.

In accordance with other embodiments of the invention, thetwo-dimensional image may be a radiograph obtained by transmission ofpenetrating radiation through the knee joint, such as by transmission ofx-rays through the knee joint. The method may further include predictinga clinical outcome of a therapeutic modality based on characterizationof the skeletal morphology in terms of parameters of the deformablestatistical template.

In accordance with further embodiments of the invention, the step ofcreating a deformable statistical template may include defining the setof parameters on the basis of statistical analysis of a set oftwo-dimensional images of knees, while the step of fitting, at runtime,a plurality of loci associated with specified model features may includereceiving operator input. Steps (c) and (d) of the method recited abovemay be repeated at successive points in time for describing evolution ofthe skeletal morphology over time.

In accordance with yet further embodiments of the invention, anadditional step may include performing a clinical intervention betweensuccessive iterations of step (c). The step of parameterizing positionsmay include successive approximation of positions of the plurality ofloci. The step of characterizing the skeletal morphology of the knee mayinclude estimating the joint separation width at a specified position inthe medial or lateral compartment, or estimating the minimum jointseparation in at least one of the medial and lateral compartment.

A further aspect of the invention provides a method for characterizing aknee joint in terms of its skeletal morphology. This method has stepsof:

a. fitting, at runtime, in a two-dimensional image of the skeleture of aknee, a plurality of loci associated with specified features to allowparameterization of a deformable statistical template;

b. parameterizing positions of the plurality of loci in a given subjectto derive parameters of the deformable statistical template; and

c. characterizing the skeletal morphology on the basis of either asubset of the plurality of loci, and/or the derived parameters of thedeformable statistical template.

Finally, in accordance with the invention, a computer program productmay be provided for use on a computer system for characterizing theskeletal morphology of a knee joint of a subject. The computer programproduct has program code for storing loci associated with specifiedskeletal features in a two-dimensional image of a knee joint into acomputer memory, program code for parameterizing positions of theplurality of loci in a given subject to derive parameters of adeformable statistical template, and program code for characterizing theskeletal morphology on the basis of either a subset of the plurality ofloci, and/or the derived parameters of the deformable statisticaltemplate.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the invention will be more readily understoodby reference to the following detailed description, taken with referenceto the accompanying drawings, in which:

FIG. 1 depicts the prior art standard measurement of the mJSW in themedial compartment as surrogate measure of knee osteoarthritis;

FIG. 2 depicts a typical set of anatomical landmarks defined forapplication of the invention;

FIG. 3 is a flow chart depicting an application of preferred embodimentsof the invention to image data of a knee; and

FIG. 4 depicts software analysis of specified measures of knee jointmorphology, in accordance with preferred embodiments of the presentinvention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

In accordance with preferred embodiments of the current invention, acomputer analysis of a digitized knee radiograph is carried out eitherautomatically or semi-automatically using a deformable statisticaltemplate that has been produced, for example, by the statisticalanalysis of a number of hand-annotated example radiographs of the knee.

The invention described herein and claimed in any appended claims isapplied to data obtained by imaging of a knee joint, of a person oranimal, by the use of penetrating electromagnetic radiation such asx-rays, for example. Typically, two-dimensional radiographs representingthe transmission of penetrating radiation through the joint areemployed. While it is to be understood that the invention is not limitedin scope to a particular modality of imaging nor to a particularmodality for storing and Manipulating the image, or images, obtained,there are advantages that arise from particular modalities, such as thehigh spatial resolution advantageously provided by high energy (x-ray orgamma ray) radiation.

Analysis of the image of the knee joint (referred to, herein, withoutlimitation, as a ‘radiograph’) proceeds, as described below, on thebasis of a ‘model’ which is applied to the input data. As used hereinand in any appended claims, the term ‘model,’ generally, refers to anymathematical description that provides for parameterization of theposition and/or motion of a subject or its component parts. Theapplication of the methods described herein to any model of knee imagedata is within the scope of the present invention as claimed. When amodel is referred to herein as “statistical,” it is to be understood asbased on an analysis of variation of parameters among members of apopulation of subjects.

More particularly, the invention will be described with reference to aclass of models wherein the model represents the average relativepositions of a specified set of 2D point positions on the knee, alongwith a mathematical description of the way these relative positions varyin normal circumstances among individuals or in a particular individualwith the passage of time or due to an intervening circumstance, such,for example, as the progression of a disease. Practice of the presentinvention is posited upon the existence of a mathematical model of‘plausible’ morphologies, wherein morphology encompasses shapes andshape variation, and may also encompass other aspects of appearance suchas the texture of a modeled object. A method, described below, isemployed for applying the model to data obtained from an image of anactual knee. The method is not, however, specific to any particularplacement of the point set, and is illustrated in FIG. 2, purely by wayof example, and without limitation, as a set of points (or ‘landmarks’)20 placed automatically, or semi-automatically, on the tibial spines,peripheral boundaries of the joint, margins of the femoral condyles andtibial plateau. A ball-bearing 25, used as a calibration target of knowndiameter, to allow measurements to be expressed in standard units oflength, may also be found in the image shown in FIG. 2.

During run-time application of embodiments of the present invention, thespecified points are preliminarily identified (a process referred to,herein, as segmentation), in an image of a knee joint, by a programelement trained to identify these positions. In semi-automatic analysis,the user of the application is asked to define some subset (proper orfull) of the landmarks on the knee radiograph (larger dots 26 in FIG. 2)that were identified, either automatically or semi-automatically, increation of the deformable statistical template. These positions aredefined in such a manner as to effectively ‘describe’ the radiographicappearance of the knee—whether by relation to extremal features orotherwise.

Even though the precise morphology of the knee joint varies amongsubjects and changes with time, these landmarks remain identifiable, forthe most part. The template is statistical in that it models thedistribution (with the mean and ‘normal’ variation, or other momentsserving, without limitation, as representative characterizations) of theradiographic appearance (as discussed above) of the knee across anensemble of subjects. The template, thus, allows for parameterization ofthe morphology in terms of a finite number of values, with the presentinvention independent of any particular scheme of parameterization.

A mathematical model of the plausible positions of points may be built,for application in the present invention, as now described. A set oftraining 2D data blocks, are taken from an ensemble of radiographicimages of knees. These data may be augmented by manual adjustment priorto the process of model building.

For the purpose of building a model, the relative positions of the 2Dpoints are consequential rather than their ‘absolute’ space-referencedpositions. Thus, in building the model, the first step is typically toalign each frame of 2D data to a common reference frame, as may beachieved by using one of various standard alignment techniques, such asby ‘Procrustes Analysis’, which is described by Horn, Closed FormSolution of Absolute Orientation Using Unit Quaternions, J. OpticalSociety, vol. A 4, pp. 629-42 (April, 1987), which is incorporatedherein by reference.

The model provides for a compact mathematical description of thevariation in relative 2D point positions among frames of the trainingdata. Once the data are aligned, this can be done by one or more ofseveral types of statistical modeling techniques, including, forexample, ‘Principal Component Analysis’ as described by Johnson andWichern, in Applied Multivariate Statistical Analysis, pp. 458-513(5^(th) Edition, 2002).

In one set of embodiments, the model may consist of an ‘average’ shapefor the 2D data along with a set of mathematical functions whichdescribe how the shapes can change. By feeding a vector of controlnumbers or ‘model parameters’ into the mathematical functions anyplausible set of 2D point coordinates can be generated. While the modelparameters may span a space of model shape excursions, such is notnecessarily the case for practice of the invention as claimed. Moreover,the model may be linear, in the sense in which motions correspond tolinear combinations of points moving along straight lines (rather than,for example, arcs or curves). However, the invention is not limited inits applicability to such models.

As will now be discussed with reference to the flow diagram of FIG. 3,embodiments of the present invention use the model, once trained asheretofore described, to segment the image, i.e., to locate the 2D pointcoordinates that characterise the skeletal morphology of the knee. Inaccordance with preferred embodiments of the invention, a number of setsof putative input point locations are generated, such as randomly oracross a set of predefined possible locations, for example. Each ofthese sets is tested in order to identify a suitable set of initialinput point locations based upon their positioning within ‘distances’ ofneighboring points that the model recognizes as ‘reasonable.’ The term‘distance’, as used herein and in any appended claims refers to a normwith respect to the parameterized variables of the model, and maycorrespond to a Euclidean norm, but need not, within the scope of theinvention. Once initial input 2D point locations have been identified,the best set of alignment parameters is found, to match these locationswith the locations of corresponding points in the model, i.e., totransform all coordinates to the reference frame of the model, in such away as to maximize the probability that the model parameters describethe actual image. Iterations, as described below, are then employed forlocalized fitting. An algorithm for performing such a segmentation stepis described in T. F. Cootes and C. J. Taylor, Statistical Models ofAppearance for Medical Image Analysis and Computer Vision, in Proc. SPIEMedical Imaging, (2001), appended hereto and incorporated herein byreference.

An initial set of points can be described as a vector X,X={x₁, x₂ . . . x_(n), y₁, y₂ . . . y_(n)},where (x_(i),y_(i)) are the 2D coordinates of the point with index i.

The points when aligned to the reference frame of the model using, e.g.,Horn (supra) are described as a vector X′ where X′ is the result ofapplying the computed alignment transformation, T, to X,X′=T(X),where T is the matrix of computed transformation parameters.

The model is some function, F, which generates a vector of parameters,b, given a set of input point coordinatesb=F(X′)

In one set of embodiments, where the model consists of an ‘average’shape for the 2D data along with a set of mathematical functions whichdescribe how the shapes can change, b is calculated using:b=A(X′−X′ _(m))where X_(m) is the vector of 2D point coordinates for the ‘average’shape and A is a matrix learned during the training phase using, forexample, Principal Components Analysis, as described in ‘PrincipalComponent Analysis’ as described by Johnson and Wichern, in AppliedMultivariate Statistical Analysis, pp. 458-513 (5^(th) Edition, 2002)which is incorporated herein by reference.

To estimate a set of point coordinates given a set of model parametersthe ‘inverse’, (which, in most cases, can only be an approximateinverse) of F, F′ is usedX _(e) ′=F′(b)

Where X_(e) is the estimated value of the 2D coordinates for a given setof parameters, b. If the model is built using Principal ComponentsAnalysis then this is written as:X _(e) =X _(m) +A′(b)Where A′ is the pseudoinverse of A which in the case of PrincipalComponent Analysis is identical to the transpose of A.

Various model-fitting algorithms may be used to accomplish the foregoingstep. In one embodiment, a simple, unweighted least squares estimate ofthe model values is computed:b=A(X′−X _(m)′)These values are used predict the values of the entire 2D point vectorin the model frame of reference according to:X _(e) ′=F′(b)

T′, the inverse of the transformation matrix T, is used to estimate theentire 2D point vector in the original frame of reference:X _(e) =T′(X _(e)′)

This subsequent set of points is now realigned with the model frame ofreference and the process that has been described is repeated. A bestset of alignment parameters is found and then the fitting algorithm isapplied to derive a best set of model parameters. The best set of modelparameters is then used to generate another set of points.

This iterative process is repeated until there is convergence (within aspecified criterion) or else until a specified maximum number ofiterations have been executed. When the iterations have finished, theoutput of the final step is a solution for the full set of 2D points asfit by the model parameters.

A final segmentation (i.e., identification, in the radiograph, of thespecified initialization points) may now be used to extract a number ofmeasurements from the radiograph, such as those are outlined below,which are presented as examples only and not as a comprehensive set:

-   -   1. The mJSW in either the lateral or medial compartment.    -   2. The JSW at any position in the medial or lateral compartment,        the position of the JSW measurement may be parameterized along a        line from the tibial spine to a specified position at an edge of        the joint, thus this measurement may be compared at various time        points in a longitudinal study.    -   3. A defined measure, having the dimensions of an area,        characterizing a specified region subtended by either        compartment.

Since a deformable statistical template has been used to detect andannotate the joint, a parameterization of the joint shape may bedetermined from optimized fit of this template. Therefore, the ‘shape’,in an abstract sense, of the joint may be compared to that of a‘universe’ of ‘normal’ joints, or else the changes in shape parametersat time points in a longitudinal study may be used as a novelmeasurement of disease progression. Changes may be mapped in specifiedmeasures over the course of a period of time, whether in the presence ofa medical intervention, or otherwise. The case of a medicalintervention, in the most general sense, will be referred to herein, andin any appended claims, as a “therapeutic modality,” and will includethe administration of medicinal agents, but will not be limited thereto.

A screenshot of a software application demonstrating several of thesemeasurements being performed is shown in FIG. 4. In particular, thefollowing measures are examples of measures that may be employed, inaccordance with the invention, for characterization of knee morphology:

Cartilage Area Measurement

For both baseline and follow-up images, and for either compartment, anarea is measured, defined by the tibial plateau, the femoral condyle andthe joint space widths (JSWs) at either end of the compartment.

Joint Space Width (JSW) Profile Measurement

For both baseline and follow-up images, and for either compartment, aprofile of Joint Space Width (JSW) may be measured along the entirelength of the tibial plateau. The JSW at a given point is the minimumdistance between the tibial boundary and the femoral boundary. The JSWprofile is measured (in mm) as a function of the distance along themedial axis of the joint from the tibial spine.

Minimum JSW Measurement

For both baseline and follow-up images, a minimum JSW may be measured inboth the medial and the lateral compartment. The minimum JSW is theminimum value of the JSW profile measurement in a given range along thetibial plateau. By default, the minimum is found between the innerextent of the cartilage area measurement, and the outer extent of theJSW profile measurement.

Equivalent JSW Measurement

For follow-up images, and for either compartment, the JSW may bemeasured at the estimated position (along the tibial plateau) at whichthe mJSW was calculated on the baseline image. This measurement requiresthat both baseline and follow-up images for a patient are attached tothe study.

Cross-Over Flag

The cross-over flag is a flag which indicates whether the boundary ofthe tibia crosses over the boundary of the femur, for either the medialcompartment or the lateral compartment. In these cases where cross-overis found, it may be desirable to ignore the results.

Shape Measure

For a given pair of baseline and follow-up images, the system maycalculate a statistic corresponding to how much the overall shape of theknee has changed between the baseline knee and the follow-up knee. Thehigher the value of this statistic, the more change there is betweenbaseline and follow-up. The units of the Shape Measure are mm, and thefigure corresponds to the mean amount by which each point on thesegmented knee boundary has moved between the baseline and follow-upknee, measured in the same frame of reference. This measurement requiresthat both baseline and follow-up images for a patient be attached to thestudy. This should allow the rapid identification of ‘interesting’images that may warrant extended manual investigation.

The disclosed methods for characterizing the morphology of a knee jointmay be implemented as a computer program product for use with a computersystem. Such implementations may include a series of computerinstructions fixed either on a tangible medium, such as a computerreadable medium (e.g., a diskette, CD-ROM, ROM, or fixed disk) ortransmittable to a computer system, via a modem or other interfacedevice, such as a communications adapter connected to a network over amedium. The medium may be either a tangible medium (e.g., optical oranalog communications lines) or a medium implemented with wirelesstechniques (e.g., microwave, infrared or other transmission techniques).The series of computer instructions embodies all or part of thefunctionality previously described herein with respect to the system.Those skilled in the art should appreciate that such computerinstructions can be written in a number of programming languages for usewith many computer architectures or operating systems. Furthermore, suchinstructions may be stored in any memory device, such as semiconductor,magnetic, optical or other memory devices, and may be transmitted usingany communications technology, such as optical, infrared, microwave, orother transmission technologies. It is expected that such a computerprogram product may be distributed as a removable medium withaccompanying printed or electronic documentation (e.g., shrink wrappedsoftware), preloaded with a computer system (e.g., on system ROM orfixed disk), or distributed from a server or electronic bulletin boardover the network (e.g., the Internet or World Wide Web). Of course, someembodiments of the invention may be implemented as a combination of bothsoftware (e.g., a computer program product) and hardware. Still otherembodiments of the invention are implemented as entirely hardware, orentirely software (e.g., a computer program product).

The described embodiments of the invention are intended to be merelyexemplary and numerous variations and modifications will be apparent tothose skilled in the art. All such variations and modifications areintended to be within the scope of the present invention as defined inthe appended claims.

1. A method for characterizing a knee joint in terms of a modelparameterization, the method comprising: a. creating a deformablestatistical template characterized by a set of parameters that, as aset, span an abstract vector space representing the set of spatialpositions of specified features of the knee joint, each vector uniquelydescribing its variation from a population mean; b. fitting at runtime,in a two-dimensional image of the skeleture of a knee, a plurality ofloci associated with specified features to allow parameterization interms of a deformable statistical template; c. parameterizing positionsof the plurality of loci in a given subject to derive values forparameters of the deformable statistical template; and d. characterizingthe skeletal morphology of the knee of the given subject on the basis ofeither a subset of the plurality of loci, and/or the derived parametersof the deformable statistical template.
 2. A method in accordance withclaim 1, wherein the two-dimensional image is a radiograph obtained bytransmission of penetrating radiation through the knee joint.
 3. Amethod in accordance with claim 1, wherein the two-dimensional image isa radiograph obtained by transmission of x-rays through the knee joint.4. A method in accordance with claim 1, further including predicting aclinical outcome of a therapeutic modality based on characterization ofthe skeletal morphology in terms of parameters of the deformablestatistical template.
 5. A method in accordance with claim 1, whereinthe step of creating a deformable statistical template includes definingthe set of parameters on the basis of statistical analysis of a set oftwo-dimensional images of knees.
 6. A method in accordance with claim 1,wherein the step of fitting, at runtime, a plurality of loci associatedwith specified model features includes receiving operator input.
 7. Amethod in accordance with claim 1, further comprising repetition ofsteps (c) and (d) at successive points in time for describing evolutionof the skeletal morphology over time.
 8. A method in accordance withclaim 7, further comprising a step of performing a clinical interventionbetween successive iterations of step (c).
 9. A method in accordancewith claim 1, wherein the step of fitting includes successiveapproximation of positions of the plurality of loci.
 10. A method forcharacterizing a knee joint in terms of its skeletal morphology, themethod comprising: a. fitting, at runtime, in a two-dimensional image ofthe skeleture of a knee, a plurality of loci associated with specifiedfeatures to allow parameterization of a deformable statistical template;b. parameterizing positions of the plurality of loci in a given subjectto derive parameters of the deformable statistical template; and c.characterizing the skeletal morphology on the basis of either a subsetof the plurality of loci, and/or the derived parameters of thedeformable statistical template.
 11. A method according to claim 1,wherein characterizing the skeletal morphology includes estimating thejoint separation width at a specified position in the medial or lateralcompartment.
 12. A method according to claim 1, wherein characterizingthe skeletal morphology includes estimating the minimum joint separationin at least one of the medial and lateral compartment.
 13. A computerprogram product for use on a computer system for characterizing theskeletal morphology of a knee joint of a subject, the program productcomprising: a. program code for storing loci associated with specifiedskeletal features in a two-dimensional image of a knee joint into acomputer memory; b. program code for parameterizing positions of theplurality of loci in a given subject to derive parameters of adeformable statistical template; and c. program code for characterizingthe skeletal morphology on the basis of either a subset of the pluralityof loci, and/or the derived parameters of the deformable statisticaltemplate.